Table 2
Torsion-rotation parameters needed for the global fit of transitions involving vt = 0 and vt = 1 torsional energy levels of 13C2-methyl formate (H12COO13CH3) provided in this work and comparison with the torsion-rotation parameters obtained in the former global fit of transitions only involving vt = 0 torsional states (Carvajal et al. 2009).
| nlma | Operatorb | Parameter | vt = 0,1 c | vt = 0 d | nlm | Operator | Parameter | vt = 0,1 c | vt = 0 d |
|
|
|||||||||
| 220 | (1−cos3γ) /2 | V 3 | 369.93168(395) | 407.1549(147)g | 642 | (1 − cos6γ)P2 | N v | −0.312260(869) × 10-3 | 0.0f |
|
F | 5.4785214(464) | 5.69168218e |
|
K 2 | 0.84669(480) × 10-3 | 0.0f | ||
| 211 | P γ P a | ρ | 0.084337567(345) | 0.0845207(106) |
|
c 11 | −0.161265(889) × 10-3 | 0.0f | |
| 202 |
|
A RAM | 0.58658923(178) | 0.5857484(245) | (1 − cos6γ)(PaPb + PbPa) | d d ab | −0.29738(147) × 10-3 | 0.0f | |
|
B RAM | 0.29682136(198) | 0.2959971(182) |
|
M v | 0.7960(365) × 10-8 | 0.0f | ||
|
C RAM | 0.173496850(137) | 0.1729010(134) | 2  |
c 3 | 0.13176(197) × 10-7 | 0.0f | ||
| (PaPb + PbPa) | D ab | − 0.15976497(192) | − 0.1573691(747) | 624 | (1 − cos3γ)P4 | f v | 0.91080(149) × 10-8 | 0.0f | |
| 440 | (1−cos6γ) /2 | V 6 | 25.40353(193) | 0.0f |
|
k 5J | 0.4484(183) × 10-7 | 0.0f | |
| 422 |
|
G v | 0.27105(240) × 10-5 | 0.4682(101) × 10-4 |
|
k 5K | −0.21242(275) × 10-6 | 0.0f | |
|
c 1 | 0.10489(207) × 10-5 | 0.0f | (1 − cos3γ)(PaPb + PbPa)P2 | d abJ | 0.46277(344) × 10-7 | 0.9060(708) × 10-7 | ||
| sin3γ(PaPc + PcPa) | D ac | 0.0f | − 0.0040623(839) |
|
d abK | −0.83350(642) × 10-7 | 0.3349(260) × 10-6 | ||
| sin3γ(PbPc + PcPb) | D bc | 0.00074120(917) | 0.0010563(383) |
|
c 2K | 0.47452(372) × 10-7 | 0.0f | ||
| (1 − cos3γ)P2 | F v | − 0.00229820(140) | − 0.0007557(425) |
|
k 2J | 0.4462(154) × 10-9 | 0.0f | ||
|
k 5 | 0.01046256(804) | 0.0124250(566) |
|
c 1K | 0.18733(536) × 10-9 | 0.0f | ||
|
c 2 | −0.3062(148) × 10-4 | 0.0f | sin3γ(PbPc + PcPb)P2 | D bcJ | −0.12682(268) × 10-7 | 0.0f | ||
|
k 2 | −0.43892(170) × 10-4 | 0.0f | 606 | P 6 | H J | −0.755(12) × 10-12 | −0.31(1) × 10-13 | |
| (1 − cos3γ)(PaPb + PbPa) | d ab | − 0.00573380(154) | − 0.013852(236) |
|
H JK | 0.10555(83) × 10-10 | 0.0f | ||
|
Δab | 0.0f | −0.16792(565) × 10-3 |
|
H KJ | −0.34983(244) × 10-10 | 0.0f | ||
| 413 | P γ P a P 2 | L v | 0.1824(134) × 10-6 | −0.2045(247) × 10-5 |
|
H K | 0.50362(252) × 10-10 | 0.0f | |
|
k 1 | 0.127972(329) × 10-4 | 0.0f |
|
h J | −0.364(6) × 10-12 | 0.0f | ||
|
c 4 | 0.94726(730) × 10-6 | 0.39452(688) × 10-5 |
|
h JK | 0.1996(22) × 10-11 | 0.1130(25) × 10-11 | ||
|
δ ab | −0.343262(938) × 10-5 | 0.1707(107) × 10-4 |
|
h K | −0.1811(68) × 10-11 | 0.0f | ||
| 404 | − P4 | ΔJ | 0.24016(201) × 10-6 | 0.15312(163) × 10-6 | P4(PaPb + PbPa) | D abJJ | 0.2077(52) × 10-11 | 0.0f | |
|
ΔJK | −0.235426(785) × 10-5 | 0.21223(170) × 10-5 |
|
D abJK | −0.10787(148) × 10-10 | 0.0f | ||
|
ΔK | 0.576749(422) × 10-5 | −0.17369(181) × 10-5 | 615 | P γ P a P 4 | l v | 0.14903(534) × 10-10 | 0.0f | |
|
δ J | 0.8245(100) × 10-7 | 0.39739(813) × 10-7 | ||||||
|
δ K | −0.41365(637) × 10-7 | 0.108794(621) × 10-5 | ||||||
| P2(PaPb + PbPa) | D abJ | −0.48884(361) × 10-6 | 0.24287(221) × 10-6 | ||||||
|
D abK | 0.1345545(843) × 10-5 | 0.13608(491) × 10-5 | ||||||
Notes.
Notation from Ilyushin et al. (2003); n = l + m, where n is the total order of the operator, l is the order of the torsional part and m is the order of the rotational part.
Notation from Ilyushin et al. (2003).
{ A,B } =
AB + BA. The product of the
parameter and operator from a given row yields the term actually used in the
vibration-rotation-torsion Hamiltonian, except for F, ρ and A, which occur in the
Hamiltonian in the form 
.
Values of the parameters from the present fit, for the ground torsional state vt = 0 and the first excited torsional state vt = 1. All parameter values are in cm-1 except for ρ which is unitless. Statistical uncertainties are given in parentheses in units of the last quoted digit.
Values of the parameters from the fit for the ground torsional state vt = 0 given by Carvajal et al. (2009). The 27 parameters were fitted for 936 MW lines from vt = 0 with a root mean square of 97 kHz. All parameter values are in cm-1 except for ρ which is unitless. Statistical uncertainties are given in parentheses in units of the last quoted digit.
The internal rotation constant F of HCOO13CH3 was kept fixed to the ab initio value calculated in the equilibrium structure (see Carvajal et al. 2009).
Very large effective value obtained as a consequence of fixing F parameter to a large ab initio value and because F, V3 and V6 were not able to fit them at the same time only from the ground torsional state (Carvajal et al. 2009).
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